NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Predictive Models of Li-ion 

Battery Lifetime

Kandler Smith, Ph.D.

Eric Wood, Shriram Santhanagopalan, Gi-Heon Kim, Ying Shi, Ahmad Pesaran

National Renewable Energy Laboratory

Golden, Colorado

IEEE Conference on Reliability Science for Advanced Materials and Devices

Colorado School of Mines • Golden, Colorado • September 7-9, 2014

NREL/PR-5400-62813
2

Key Messages

• Semi-empirical battery lifetime 

models are generally suitable for 

system design & control

o Long-term validation still needed

o Standardization would benefit industry

o Characterization requires expensive cell 

aging experiments

• Physics lifetime models are needed 

to reduce test time as well as guide 

future cell design

o Open questions remain how best to 

model electrochemo-thermo- mechanical processes across length- and 

time-scales

Liu et al., J. Echem Soc. (2010)

NREL 

Life & 

MSMD 

Models
3

Thermal

NREL Electrochemical/Thermal/Life Models

Multi-Scale 

Multi-Domain 

(MSMD) model

• Inter-domain 

coupling of field 

variables, source 

terms

• Efficient, flexible 

framework for 

physics expansion

• Leading approach 

for large-cell 

computer-aided 

engineering models

Kim et al. (2011) “Multi-Domain Modeling of Lithium-Ion Batteries Encompassing Multi-Physics in Varied 

Length Scales”, J. of Electrochemistry, Vol. 158, No. 8, pp. A955–A969

Electrochemical

Current Collector (Cu)

Current Collector (Al)

p

Negative

Electrode

Separator

Positive

Electrode
4

Life-predictive model

• Physics-based surrogate 

models tuned to aging test data

• Implemented in system design 

studies & real-time control

• Regression to NCA, FeP, NMC 

chemistries

15°C

20°C

25°

C

30°C

10°C

Minneapolis

Houston

Phoenix

Li-ion graphite/nickelate life:

PHEV20, 1 cycle/day 54% ∆DoD

No cooling

Air cooling

Air cooling, 

low resistance cell

Phoenix, AZ ambient conditions

33 miles/day driving, 2 trips/day

Liquid cooling, 

chilled fluid

Illustration by Josh 

Bauer, NREL

NREL Electrochemical/Thermal/Life Models

NCA = Nickel-Cobalt-Aluminum

FeP = Iron Phosphate

NMC = Nickel-Manganese-Cobalt
5

Outline

• Background – Li-ion Batteries

o Working principles

o Electrochemical window

o Degradation mechanisms

• Life Predictive Modeling

• Automotive Life Studies & Control
6

Li+

V

Working Principles

V

Neg. Electrode

Graphite

Hard carbon

Silicon

Titanate

Li foil

Pos. Electrode

LiXO2,

X = NiMnCo

 Co

 NiCoAl

LiMn2O4,

LiFeP04
7

Electrochemical Operating Window Potential vs. Li (V)

SOC

(x in LixC6 or y in Li1-0.6yCoO2)

0% SOC 100% SOC

Potential 

measured at 

cell terminals

charge

discharge

Figure credit:

Ilan Gur (ARPA-E) & Venkat 

Srinivasan (LBNL), 2007
8

Electrochemical Window – Degradation Potential vs. Li (V)

SOC

(x in LixC6 or y in Li1-0.6yCo)O2)

Figure credit: Ilan Gur (ARPA-E) & Venkat Srinivasan (LBNL) 2007
9

Negative Electrode Degradation (Graphite)

Graphene layer Graphite exfoliation, cracking

(gas formation, solvent co-intercalation)

Electrolyte decomposition

and SEI formation

SEI conversion, 

stabilization and growth

SEI dissolution, precipitation

Positive/negative interactions

Lithium plating and 

subsequent corrosion

Donor solvent

SEI

Li+ 1) Manufacturing

 environment

2) Application

 environment

 i) graceful fade

 (time at high T,SOC)

 ii) sudden fade/

 damage

 (cycling at low T)

Figure credit: Vetter et al., Journal Power Sources, 2005

Negative/ 

electrolyte 

interactions
10

Positive Electrode Degradation (Metal Oxide)

Positive/negative 

interactions

X. Xiao et al., Echem 

Comm., 32 (2013) 31-34.

Positive/electrolyte 

interactions

Figure credit: Vetter et al., Journal Power Sources, 2005
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Mechanical Coupled Stress & Degradation

• Least understood 

amongst ECTM 

physics

Figure credit: Santhanagopalan, Smith, et al., Artech House (in press)
12

Mechanical Coupled Stress & Degradation

• Examples

Cannarella, J. Power Sources (2014)

Diercks, Packard, 

Smith et al., J. Echem 

Soc (2014)

Figure credit: Santhanagopalan, Smith, et al., Artech House (in press)
13

Outline

• Background – Li-ion Batteries

• Life Predictive Modeling

o Physics-based

o Semi-empirical

• Automotive Life Studies & Control
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Degradation Mechanism vs. Length Scale

 

 

 

 

 

 

 

 

 

 

 

10-10 10-8 10-6 10-4 10-2 10-0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Chemistry

• SEI growth

• Li plating

• Electrolyte 

decomposition

• Gas generation

Particle scale

• SEI μ-cracking

• Fracture, damage 

of transport paths

• Phase evolution, 

voltage droop

Electrode scale

• Electrode creep, 

delamination, 

isolation

• Separator pore 

closure

• Pore clogging

Cell scale

• 3D elec, thermal, 

mech. inhomogeneities

• Tab effects

• Stack/wind Module scale

• Thermal & 

mechanical 

boundary conditions
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Macro-scale Stress Model

 

 

 

 

 

 

 

 

 

 

 

10-10 10-8 10-6 10-4 10-2 10-0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

• Stress/strain due to thermal 

and electrode bulk 

concentration changes

• Coupled echem & thermal

Behrou, Maute, Smith, ECS Mtg. (2014)
16

Micro-scale Stress/Degradation Model

 

 

 

 

 

 

 

 

 

 

 

10-10 10-8 10-6 10-4 10-2 10-0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Damage 

evolution

Performance impact

An, Barai, Smith, Mukherjee, JES 2014
17

NREL Life Predictive Model

•Data: J.C. Hall, IECEC, 2006.

17

Relative Capacity 

(%)

Time (years)

r2 = 

0.942

Li-ion NCA chemistry

Arrhenius-Tafel-Wohler model 

describing a2(∆DOD,T, V)

NCA

• Correct separation of calendar vs. cycling degradation for 

extrapolation of 1⁄2 year testing to 10+ year life

• Extensible to untested drive cycles, environments (state form)

Relative

Resistance

Relative

Capacity

Qsites = c0 + c2 N + ...

R = a1 t z + a2 N

Calendar fade

• SEI growth 

• Loss of cyclable lithium 

• Coupled with cycling

• a1, b1 = f(∆DOD,T,Voc,...)

Q = min ( QLi , Qsites )

QLi = b0 + b1 t z + ...

Cycling fade

• Active material structure 

 degradation and 

 mechanical fracture

• a2, c2 = f(∆DOD,T,Voc ,...)

NCA
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Knee in Fade Critical for Predicting End of Life

Example simulation: 

1 cycle/day at 25°C 50% DOD:

Graceful fade 

controlled by

Li loss ~ t1/2

80% DOD:

Transitions to 

electrode site loss, 

N ~ 2300 cycles

Life over-predicted by 25% without accounting for 

transition from Li loss (~chemical) to site loss 

(~mechanical)

NCA

Time (Days)
19

Electrode Site Loss – Cell Aging Data

• Graphite/iron-phosphate meta-dataset from multiple labs

FeP
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Electrode Site Loss – Cell Aging Data

• Graphite/iron-phosphate meta-dataset from multiple labs

• 13 of 50+ test conditions show apparent “knee” in capacity 

 fade curve

FeP
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Electrode Site Loss Model (graphite/iron phosphate)

exp( ( ))[ ] exp( ( ))( ) . , ,

binder intercal.

1 1

1 2 3 R

1 1

2 2, 









 



 



 = − + ∆ + − − −

pulse ref

pulse

rate ref

rate

ref

a

ref

a

t

t

C

C

T T

E

R T T

E

c c ref m DOD m T m

min( , ). Li sites q = q q

q b b t b N z

Li

= 0 + 1 + 2 qsites

= c0 + c2N

accelerated 

polymer failure at 

high T

bulk

intercalation

strain

bulk

thermal

strain

intercalation gradient strain, accelerated 

by low temperature 

FeP

Model successfully 

describes 13 aging 

conditions from 0°C 

to 60°C
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Outline

• Background – Li-ion Batteries

• Life Predictive Modeling

• Automotive Life Studies & Control

o Temperature (xEV)

o Charge control (xEV / grid)

o Prognostic/duty-cycle control (xEV)
23

Ambient Effects on Battery Average Temperature

0

5

10

15

20

25

30

35

Phoenix, AZ Los Angeles,

CA

Minneapolis,

MN

Temperature (C)

BEV75

Passive cooling

Average Ambient w/ solar effects

w/ driving effects

0

5

10

15

20

25

30

35

Phoenix, AZ Los Angeles,

CA

Minneapolis,

MN

Temperature (C)

PHEV35

Chilled liquid cooling

Average Ambient w/ solar effects

w/ driving + active TMS

• Ambient conditions dominate

• Thermal connection with passenger 

cabin, parking in shaded structures 

strongly influence battery life

• Battery temperature and 

lifetime weakly coupled to 

ambient conditions
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Optimized Charging Strategies

• Reduce time spent at high SOC (delay charging)

• Avoid high C-rates to lower peak temperatures

Cost 

function

CU-Boulder/Hoke (2014) 
25

Optimized Charging Strategies

• Delayed charging best

Begin charge End charge

A) Constant energy cost

• Response to price signals

• No V2G energy exported until electricity price $0.50/kWh

Begin charge End charge

B) Variable energy cost
26

NREL ARPA-E AMPED Projects in Battery Control

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Utah State/Ford

Project: 20% reduction in 

PHEV pack energy content 

via power shuttling system 

and control of disparate 

cells to homogenous endof-life

NREL: Requirements 

analysis; life model of 

Ford/Panasonic cell; 

controls validation of Ford 

PHEV packs

Eaton Corporation

Project: Downsized HEV 

pack by 50% through 

enabling battery prognostic 

& supervisory control while 

maintaining same HEV 

performance & life

NREL: Life testing/modeling 

of Eaton cells; controls 

validation on Eaton HEV 

packs

Washington Univ.

Project: Improve available 

energy at the cell level by 

20% based on real-time 

predictive modeling & 

adaptive techniques

NREL: Physics-based celllevel models for MPC; 

implement WU 

reformulated models on 

BMS; validate at cell & 

module level

AMPED = Advanced Management and Protection of Energy Storage Devices
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NREL ARPA-E AMPED Projects in Battery Control

Utah State/Ford

Project: 20% reduction in 

PHEV pack energy content 

via power shuttling system 

and control of disparate 

cells to homogenous endof-life

NREL: Requirements 

analysis; life model of 

Ford/Panasonic cell; 

controls validation of Ford 

PHEV packs

1C Energy (Wh)

Teardown analysis of automotive pack aged to 70% 

remaining energy shows ±5.5% variation at EOL 

±5.5% variation at EOL

• Active balancing most benefits energy applications with large cellto-cell disparity

• Key question: How much does cell-to-cell disparity grow with age?

Extreme driving conditions, large pack ΔT cause 

abnormally large cell capacity imbalance growth
28

Summary

• Main factors controlling battery lifetime

o Time at high T & SOC (weak coupling with DOD & C-rate)

o Cycling at high DOD & C-rate; Low/high T & SOC

• Semi-empirical battery lifetime models are 

generally suitable for system design & control

o NREL models describe various commercial chemistries

o Life extensions of 20% to 50% may be possible

• Physics lifetime models to provide design feedback

o Electrochemical/thermal processes well understood

o Mechanics coupling underway at various length scales
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Funding

• US Dept. of Energy – Vehicle Technologies Office: Brian Cunningham, David 

Howell

• US Dept. of Energy – Advanced Research Projects Agency: Ilan Gur, Patrick 

McGrath, Russel Ross

• US Army Tank Automotive Research, Development & Engineering Center: 

Yi Ding, Sonya Zanardelli, Matt Castanier

Collaborators

• Texas A&M University: Partha Mukherjee, Pallab Barai, Kai An

• University of Colorado at Boulder: Kurt Maute, Reza Behrou, Dragan 

Maksimovic, Andrew Hoke

• Colorado School of Mines: Corinne Packard, David Diercks, Brian Gorman

• Eaton Corporation: Chinmaya Patil

• Utah State: Regan Zane

• Ford Motor Company: Dyche Anderson

Acknowledgements
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Thank you